The Colombia defender has been the subject of negotiations between the two clubs for several weeks.
Lucumi has already accepted Sunderland's contract offer of five years worth €3m-a-season - net, says Il Corriere dello Sport.
However, while Bologna are prepared to do business with Sunderland, they're insisting no sale will happen until they find a replacement.
Juventus veteran Daniel Rugani has emerged as an option for Bologna in recent hours.
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